Non-equilibrium Fluctuations in a Ternary Mixture Subjected to a Temperature Gradient
- PDF / 501,408 Bytes
- 18 Pages / 439.37 x 666.142 pts Page_size
- 22 Downloads / 210 Views
Non-equilibrium Fluctuations in a Ternary Mixture Subjected to a Temperature Gradient José M. Ortiz de Zárate1 · Loreto García-Fernández2,3,4 · Henri Bataller4 · Fabrizio Croccolo4 Received: 20 December 2019 / Accepted: 13 April 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We present the complete theory for the decay rates of non-equilibrium fluctuations in a ternary liquid mixture subjected to a stationary temperature gradient, when the quiescent non-convective state is stable. In the most general case, within Boussinesq approximation, four fluctuating modes exist. Depending on the parameter values, propagative modes may be present, and we discuss numerically some cases where that is so. We complete the work with a discussion of symmetry upon changes in concentration representation, as well as examination of some limiting cases with practical relevance for which analytical progress is possible. We make contact with previous publications, which were based on some kind of approximation. Keywords Fluctuating Hydrodynamics · Non-equilibrium fluctuations · Ternary systems · Stochastic processes · Onsager regression hypothesis
1 Introduction The intensity of fluctuations in liquids in non-equilibrium (NE) states, like when subjected to a temperature gradient, can be orders of magnitude larger than around the equivalent equilibrium state at the average temperature [1,2]. This is physically due to a coupling between the temperature fluctuations and the velocity fluctuations parallel to the gradi-
Communicated by Bernard Derrida.
B B
José M. Ortiz de Zárate [email protected] Loreto García-Fernández [email protected]
1
Facultad de Física, Universidad Complutense, Madrid, Spain
2
Facultad de Farmacia, Universidad CEU San Pablo, Urbanización Montepríncipe, Boadilla del Monte, Madrid, Spain
3
Centre National d’Études Spatiales, Paris, France
4
Universite de Pau et des Pays de l’Adour, E2S UPPA, CNRS, TOTAL, LFCR UMR5150, Anglet, France
123
J.M. Ortiz de Zárate et al.
ent, the latter mixing regions with different local temperature [1,3]. This NE-enhancement of fluctuations was originally predicted on the basis of kinetic theory [4], and later confirmed by fluctuating hydrodynamics [5]. These theoretical predictions were soon verified by dynamic light-scattering experiments in one-component liquids [6], i.e., through the analysis of temperature fluctuations; and, later, also in binary liquid mixtures. In mixtures, a NEenhancement of concentration fluctuations is due to the presence of a concentration gradient, as it exists in transient free-diffusion processes [7], or as induced by thermodiffusion [8,9]. When external forces like gravity (buoyancy) are present, the existence of gradients (NE conditions) not only affects the intensity of fluctuations, but also their dynamics. Again, this has been first discussed in one-component liquids [10] and later in binary mixtures, both theoretically [11] and experimentally [7,12]. On this regard, the dynamic analysis of the NE fluctua
Data Loading...
